Decimals & Long Division — Challenge
Place value carries on past the point, which is why the old methods still work.
What these problems cover
These questions use 3 ideas from the course. Follow any of them for a definition, where it is taught, and what it leads to.
- Divisor — The polynomial you are dividing by.
- Remainder — What is left when the divisor no longer fits. Always lower degree than the divisor.
- Place value — What each digit is worth, depending on its column.
Problem 1
What is 2.4+3.75?
- 5.99
- 6.15
- 6.19
- 7.15
- 61.5
Worked answer
6.15
Line up the decimal points, writing 2.4 as 2.40 so both numbers have two places.
2.40+3.75 = 6.15.
Problem 2
What is 0.6× 0.4?
- 0.1
- 0.24
- 0.024
- 2.4
- 24
Worked answer
0.24
Multiply as whole numbers first: 6· 4 = 24.
Each factor has one decimal place, so the product has two: 0.24.
Multiplying two numbers smaller than 1 gives something smaller than either, which 0.24 is.
Problem 3
A phone plan costs $20 a month, plus 5 cents for each text message and 10 cents for each minute of calls. In a month with 100 texts and 40 minutes of calls, what is the bill in dollars?
- 25
- 27
- 29
- 31
- 33
Worked answer
29
100 texts at 5 cents each cost 500 cents, which is 5 dollars.
40 minutes at 10 cents each cost 400 cents, which is 4 dollars.
The bill is 20+5+4 = 29 dollars.
Problem 4
What is 7.2÷ 0.9?
- 0.8
- 0.125
- 8
- 6.48
- 80
Worked answer
8
Multiply both numbers by 10 so the divisor becomes a whole number: 7.20.9 = 729.
729 = 8. Dividing by a number less than 1 makes the result larger than 7.2, as expected.
Problem 5
What is 5-1.37?
- 3.63
- 3.37
- 3.73
- 4.37
- 4.63
Worked answer
3.63
Write 5 as 5.00 so both numbers have two decimal places.
5.00-1.37 = 3.63.
Problem 6
A shopper buys three items costing $4.95 each and pays with a $20 note. How much change is received in dollars?
- 4.85
- 5.05
- 5.15
- 5.85
- 14.85
Worked answer
5.15
Three items at 4.95 cost 3· 4.95 = 14.85 dollars.
The change is 20-14.85 = 5.15 dollars.
A quick check: 4.95 is five cents under 5, so three of them are fifteen cents under 15.
Problem 7
Write 0.125 as a fraction in lowest terms.
- 18
- 14
- 15
- 112
- 125100
Worked answer
18
Three decimal places means thousandths: 0.125 = 1251000.
Divide both parts by 125: 1251000 = 18.
Problem 8
Round 3.4567 to two decimal places.
- 3.4
- 3.45
- 3.46
- 3.5
- 3.457
Worked answer
3.46
Two decimal places means keeping the digits 3.45 and deciding from the next digit whether to round up.
The next digit is 6, which is 5 or more, so the hundredths digit rises from 5 to 6.
The answer is 3.46.